The non-oscillatory shape functions [1] is written as follows:

(1)

Where is Element Degree Limiter, Field Variable Limiter (EDL, FVL), is p-order shape functions (in this paper degree of p is 3) and , and are reference functions I used equation (40) of [1] as reference function that is

(2)

Fig. 1. 1D advective equation

Fig. 2. 1D convection-diffusion equation

Fig. 3. Grid for flow over a NACA 0012 airfoil

Fig. 4. Pressure distribution on surface of NACA 0012 airfoil, steady-state

Fig. 5. Grid for flow around a cylinder.

Fig. 6. Flow around a cylinder, steady-state

Where and are liner shape functions, by putting equation (2) in (1) and also we have

(3)

Equation (3) is non-oscillatory shape functions that will be used in this paper for CFD problems.

**Examples**

In this section, I am going to use the equation (3) as shape function for approximating a few equation and compare its result with non-constant . As first example, I approximated 1D advective equation by Point Collocation weight function, see figure (1). In second example, I approximated 1D convection-diffusion equation in by Galerkin weight function, see figure (2). In third example, I approximated 2D Euler equations for pressure distribution on surface of NACA 0012 airfoil [1] by Galerkin weight function and infinite elements for non-solid boundaries, see figure (4), and flow around a cylinder [1] by Subdomain Collocation weight function see figure (6).

**Conclusions**

As can be seen from the results, with any number of elements solutions are non-oscillatory, and when we use fine mesh (usually in CFD is used) solutions are very close together. So, using of constant EDL, FVL is useful.